1. Field of the Invention
The present invention is directed to a method for computed tomography (CT), of the type wherein, for scanning a subject with a conical ray beam emanating from a focus and with a matrix-like detector array for detecting the ray beam, the focus is moved on a spiral path around a system axis relative to the subject, with the detector array supplying output data corresponding to the received radiation, and wherein images having an inclined image plane relative to the system axis are reconstructed from output data supplied during the motion of the focus on a spiral segment. The invention also is directed to a computed tomography apparatus of the type having a radiation source having a focus from which a conical ray beam emanates, a matrix-like detector array for detecting the ray beam, the detector array supplying output data corresponding to the received radiation, an arrangement for generating a relative motion between radiation source and detector array, and a subject, and an image computer to which the output data are supplied, the means for generating a relative motion for scanning the subject with the ray beam and the two-dimensional detector array causing a relative motion of the focus with respect to the system, such that the focus moves on a helical spiral path relative to the system, axis having a central axis corresponding to the system axis, and whereby the image computer reconstructs images with an image plane inclined relative to the system axis from output data supplied during the motion of the focus on a spiral segment.
2. Description of the Prior Art
Various CT methods using conical x-ray beams are known particularly in conjunction with detector arrays having a number of lines of detector elements. The cone angle that thereby occurs as a consequence of the conical shape of the x-ray beam is taken into consideration in various ways.
In the simplest case (see, for example, K. Taguchi, H. Aradate, xe2x80x9cAlgorithm for image reconstruction in multi-slice helical CTxe2x80x9d, Med. Phys. 25, pp. 550-561, 1998; H. Hu, xe2x80x9cMulti-slice helical CT: Scan and reconstructionxe2x80x9d, Med. Phys. 26, pp. 5-18, 1999), the cone angle is left out of consideration, with the disadvantage that artifacts occur in a large number of lines, and thus a large cone angle.
Further, an algorithm referred to as the MFR Algorithm (S. Schaller, T. Flohr, P. Steffen, xe2x80x9cNew, efficient Fourier-reconstruction method for approximate image reconstruction in spiral cone-beam CT at small cone-anglesxe2x80x9d, SPIE Medical Imaging Conf., Proc. Vol. 3032, pp. 213-224, 1997) is known, the disadvantage thereof being that a complicated Fourier reconstruction was necessary and the image quality leaves much to be desired.
Exact algorithms (for example, S. Schaller, F. Noo, F. Sauer, K. C. Tam, G. Lauritsch, T. Flohr, xe2x80x9cExact Radon rebinning algorithm for the long object problem in helical cone-beam CT, in Proc. of the 1999 Int. Meeting on Fully 3D Image Reconstruction, pp. 11-14, 1999 or H. Kudo, F. Noo and M. Defrise,:Cone-beam filtered back-projection algorithm for truncated helical dataxe2x80x9d, in Phs. Med. Biol., 43, pp. 2885-2909, 1998) have also been described, which have the common disadvantage of extremely complicated reconstruction.
A method and CT apparatus of the type initially described are disclosed in U.S. Pat. No. 5,802,134. In accord therewith, in contrast, images are reconstructed for image planes that are inclined by an inclination angle xcex3 around the x-axis relative to the system axis z. As a result, the (at least theoretical) advantage is achieved that the images contain fewer artifacts when the inclination angle xcex3 is selected such that a good and optimum adaptation of the image plane to the spiral path is established, insofar as possible according to a suitable error criterion, for example minimum square average of the distance measured in z-direction of all points of the spiral segment from the image plane.
In U.S. Pat. No. 5,802,134, fan data, i.e. data registered in the known fan geometry are employed for the reconstruction, the data having been acquired with the motion of the focus along a spiral segment having the length 180xc2x0 plus the fan angle, for example 240xc2x0. The optimum inclination angle xcex3 is dependent on the slope of the spiral, and thus on the pitch p.
Fundamentally, the method disclosed in U.S. Pat. No. 5,802,134 can be employed for arbitrary values of the pitch p. However, an optimum utilization of the detector area available, and thus of the radiation dose applied to the patient for image acquisition (dose utilization) is not possible below the maximum pitch Pmax. This is because even though a given transverse slice, i.e. a slice of the subject residing at a right angle relative to the system axis z, is scanned via a spiral segment that is longer then 180xc2x0 plus fan angle, only a spiral segment having the length 180xc2x0 plus the cone angle can be utilized for values of the pitch p below the maximum pitch Pmax since the utilization of a longer spiral segment would make it impossible to adapt the image plane to the spiral path well enough.
An object of the present invention is to provide a method and a CT apparatus of the type initially described wherein the cone angle is taken into consideration and wherein the preconditions for an optimum detector utilization and thus an optimum dose utilization are also established for values of the pitch p below the maximum pitch Pmax.
This object is achieved in accordance with the invention in a method for producing a computed tomography image wherein a subject is scanned with a conical x-ray beam emanating from a focus which is detected, after attenuation by the subject, using a matrix-like detector array while the focus moves along a spiral path around the subject relative to a system axis. The detector array generates output data dependent on the radiation from the x-ray beam that is incident thereon, and the output data, for a segment of the spiral path having a length that is adequate for reconstructing a CT image, are divided into a number of datasets respectively for a number of sub-segments of the aforementioned segment. Each of these sub-segments has a length that is shorter than the length that is adequate for reconstructing a CT image. For each of the sub-segments, a number of segment images is reconstructed, the segment images being in respective planes that are inclined relative to the system axis. For each sub-segment, the segment images associated therewith are combined to form a partial image with respect to a target image plane. These partial images that arise for the respective sub-segments are then combined to form a resulting CT image with respect to the target plane.
Since in the inventive method, the spiral segment whose length suffices for the reconstruction of a CT image is divided into sub-segments whose lengths are each less then the length required for the reconstruction of a CT image, the deviations of the image planes of the segment images reconstructed with respect to the sub-segments from the spiral path along the sub-segments are very small. The segment images thus contain only very slight errors caused by deviations of the image planes of the segment images from the spiral path along the sub-segments, so that the image quality in the generation of the resulting CT image is high.
The maximum inclination of the image planes of the segment images is defined from the condition that rays for the image plane of the respective segment image must be present at both ends of the sub-segment within the measurement field.
The segment images that are not useable by themselves because the length of the sub-segments is shorter then the length required for the reconstruction of a CT image are calculated in a known way, i.e. the rays most beneficial for the image plane of the respective segment image are selected from the projections for the respective sub-segment present in parallel or fan geometry according to a suitable error criterion, and are filtered and back-projected or reconstructed with other standard methods.
The combining of the segment images belonging to a sub-segment, i.e. their reformatting onto a target image plane, leads to a sub-image that is likewise not useable by itself because of the excessively short length of the sub-segment. It is only when the sub-images of all sub-images belonging to the respective spiral segment for the desired target image plane are combined to form a resulting CT image does a useable image arise, since the overall length of the spiral segment derived from the sub-segments suffices for the reconstruction of a CT image.
The image quality of this image is especially high when the segment images are reconstructed for image planes that are inclined around a first axis intersecting the system axis at a right angle by an inclination angle "khgr" as well as around a second axis intersecting each of the first and the system axis at a right angle by a tilt angle xcex4 with respect to the system axis because the adaptation of the image planes of the segment to the spiral path of the respective sub-segment is then better again.
In an embodiment of the invention, the neighboring sub-segments overlap, so the output data belonging to the overlap regions are respectively weighted such that the weights of output data corresponding to one another in the overlapping sub-segments produce a value of one.
The advantage of overlapping sub-segments is that artifacts that would otherwise occur at the adjoining edges of the sub-segments are avoided.
In an embodiment, segment images for a number nima of inclined image planes are reconstructed for each sub-segment, whereby the image planes have different z-positions zima. Due to the reconstruction of a number of segment images having differently inclined image plane for different z-positions, it is possiblexe2x80x94by a suitable selection of the inclination angle xcex3 and of the tilt angle xcex94xe2x80x94to optimally adapt the image plane of the respective segment image for each of these z-positions to the sub-segment and to thus utilize the detector array as well as the dose completely in theoretical terms and to the greatest extent in practice. In a preferred embodiment of the invention, the number of inclined image planes intersect in a straight line that proceeds tangentially relative to the sub-segment.
In order to obtain an optimally complete detector utilization and dose utilization, the following applies according to a version of the invention for the extreme values +xcex4max and xe2x88x92xcex4max of the tilt angle xcex4 of the inclined image planes belonging to a sub-segment:       ±          δ      max        =      arctan    ⁢          (                                    WM            2                    +                                    Sp              ⁢                                                α                  1                                                  2                  ⁢                  π                                                      ±                          RFOV              ⁢                              xe2x80x83                            ⁢              cos              ⁢                              xe2x80x83                            ⁢                              α                1                            ⁢              tan              ⁢                              xe2x80x83                            ⁢                              γ                0                                                                          -                                          R                f                                            cos                ⁢                                  xe2x80x83                                ⁢                                  γ                  0                                                              -                                    (                              ±                RFOV                            )                        ⁢                                          sin                ⁢                                  xe2x80x83                                ⁢                                  α                  1                                                            cos                ⁢                                  xe2x80x83                                ⁢                                  γ                  0                                                                        )      
wherein xcex30 is the value of the inclination angle xcex3 determined for the tilt angle xcex4=0 according to       γ          0      =      tan        ⁢      (                            -          Sp                ⁢                  xe2x80x83                ⁢                  α          ⋒                            2        ⁢        π        ⁢                  xe2x80x83                ⁢                  R          f                ⁢        sin        ⁢                  xe2x80x83                ⁢        α              )  
For a high image quality, in another version of the invention the optimum value xcex3min of the inclination angle belonging to a given amount |xcex4max| of the maximum value of the tilt angle xcex4 is determined such that an error criterion is met, for example minimum average of the squares the respective spacings of all points of the sub-segment from the image plane measured in the z-direction, is met.
If the rotational axis, around which the focus rotates around the system axis, is not identical with the system axis but intersects the system axis at an angle referred to as a gantry angle xcfx81, then the following applies to the inclination angle xcex3xe2x80x2 to be selected:       γ    xe2x80x2    =      arctan    ⁢                            Sp          ·          cos                ⁢                  xe2x80x83                ⁢        ρ                                          4            ⁢                                          π                2                            ·                              R                f                                              +                                    S              2                        ⁢                          P              2                                +                      4            ⁢                          π              ·                              R                f                                      ⁢            cos            ⁢                          xe2x80x83                        ⁢            α            ⁢                          xe2x80x83                        ⁢            sin            ⁢                          xe2x80x83                        ⁢                          ρ              ·              Sp                                          
Here, as well, there is the possibility of determining the appertaining optimum value of the inclination angle xcex3xe2x80x2 for a given magnitude of the maximum value of the tilt angle |xcex4max| such that an error criterion, for example minimum average of the squares of the respective spacings of all points of the sub-segment from the image plane measured in the z-direction.
In order to obtain an optimally complete detector and dose utilization, the following is also valid according to a version of the invention for the number nima of the inclined image planes, for which segment images with inclined plane are generated for each sub-segment:       n    ima    =      floor    ⁡          [              sM        p            ]      
wherein s is the length of the sub-segments.
Likewise for an optimally complete detector and dose utilization, the tilt angles xcex4 of the inclined image planes are determined in a version of the invention according to       δ    ⁢          (      i      )        =            δ      max        ⁢                            2          ⁢          i                -                  (                                    n              ima                        -            1                    )                                      n          ima                -        1            
given the condition of detector lines of equal width.
In order to create the conditions for obtaining transverse tomograms to which the users of CT apparatus are accustomed, a reformatting is provided according to one version of the invention, i.e. a sub-image is generated in a further method wherein a number of segment images are combined. In an embodiment of the invention, it may occur that a number of segment images are combined to form a sub-image by interpolation or by, in particular, weighted averaging.
The reconstruction slice thickness of the sub-images, and thus of the resulting CT image is set according to a preferred embodiment of the invention by weighting the segment images according to the desired reconstruction slice thickness of the sub-image in the combining to form a sub-image.
In the combination of a number of segment images to form a sub-image, there is the possibility according to a preferred version of the invention of selecting the number of segment images that are combined for generating a sub-image according to the desired reconstruction slice thickness of the sub-image. For an optimally high image quality, there is the possibility of reconstructing the segment images with the least possible slice thickness.
A desired reconstruction slice thickness of a sub-image can be set according to another preferred version of the invention by selecting the number of segment images for generating a sub-image according to the following equation:
NM=2xc2x7max(z*,supxcfx86xcex94zR)/Wxc2x7NS 
The combining of the sub-images into the resulting CT image preferably ensues by addition, also preferably for a target image plane that intersects the system axis at a right angle. The target image plane, however, also can be inclined relative to the system axis.
In order to keep the amount of data arising in the generation of the segment images within limits, in a version of the invention the data corresponding to the segment images are compressed.
In a preferred embodiment of the invention the compressed data corresponding to the segment images exhibit a non-uniform pixel matrix such that the resolution in a first direction, proceeding essentially in the direction of the reference projection direction belonging to the respective sub-segment, is higher then in a second direction that proceeds essentially orthogonally relative to the reference projection direction. Such a procedure is possible because the information density and the segment images orthogonally to the reference projection direction belonging to the respective sub-segment is significantly greater than in the reference projection direction belonging to the respective sub-segment.
In a version of the invention, the realization of a non-uniform pixel matrix is especially simple when the compressed data corresponding to the segment images are pixels having an oblong shape, particularly rectangular pixels, with the longest extent of each pixel proceeding essentially in the direction of the reference projection direction belonging to the respective sub-segment.
Because it is time-saving, it is especially advantageous, according to another preferred embodiment of the invention, to reconstruct the segment images in the non-uniform pixel matrix, since significantly fewer pixels need to be reconstructed than in the case of a uniform pixel matrix that has the same resolution in the reference projection direction belonging to the respective sub-segment. The back-projection has an especially simple form when the back-projection direction essentially corresponds to the direction of the reference projection direction belonging to the respective sub-segment.
Since the resulting CT image exhibits a uniform pixel matrix in the usual way, the compressionxe2x80x94if it is based on the employment of a non-uniform pixel matrixxe2x80x94must be reversed according to a version of the invention no later than during the combining of the sub-images to form the resulting CT image.
The above object also is achieved in a computed tomography apparatus operating according to the inventive CT method described above. The comments and discussion above relating to the inventive CT method apply equally to the inventive CT apparatus.